= Reduced elastic modulus
{title2=$E^*$}
The <reduced elastic modulus> combines the elastic compliance of two contacting <isotropic> bodies:
$$
\frac1{E^*}=\frac{1-\nu_1^2}{E_1}+\frac{1-\nu_2^2}{E_2}.
$$
Here $E_i$ is each body's <Young's modulus> and $\nu_i$ its <Poisson's ratio>. Both bodies deform under the same contact load, so their contributions to the indentation add. The factors involving <Poisson's ratio> account for the lateral constraint inherent in the local contact geometry.<CompuTiX Hertz contact documentation>[Hertz theory, Resulting force: effective modulus of the two bodies]{ref}
For identical materials, $E^*=E/[2(1-\nu^2)]$; against an effectively rigid probe, $E^*=E/(1-\nu^2)$ for the specimen. Thus even with a rigid probe, an indentation fit does not directly return <Young's modulus>. This matters when comparing <Hertzian contact> measurements with <tensile testing>, which imposes a different pattern of <stress>.
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